In the second case, we are given that \(g\)  is contained in a finite reflection group \(W\) .
We then write \(g_*=r_{v_1}\circ \cdots \circ r_{v_m}\)  for certain \((-2)\) -vectors \(v_1,\dots , v_m\)  in \(R_G\) . According to Lemma 3 of [1]}, we then may take the \(v_i\)  to be linearly independent, so that \(m=\nu (p-1)\) .
